### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 15 |

Publication status | Published - Dec 2011 |

### Publication series

Name | Memorandum / Department of Applied Mathematics |
---|---|

Publisher | University of Twente, Department of Applied Mathematics |

No. | 1963 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 1874-4850 |

### Keywords

- IR-78766
- METIS-281614
- EWI-20929
- Solution concept
- TU game
- Nucleolus
- Communication and conference structure

### Cite this

*The prenucleolus for games with communication structures*. (Memorandum / Department of Applied Mathematics; No. 1963). Enschede: University of Twente, Department of Applied Mathematics.

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*The prenucleolus for games with communication structures*. Memorandum / Department of Applied Mathematics, no. 1963, University of Twente, Department of Applied Mathematics, Enschede.

**The prenucleolus for games with communication structures.** / Khmelnitskaya, Anna Borisovna; Sudhölter, Peter.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - The prenucleolus for games with communication structures

AU - Khmelnitskaya, Anna Borisovna

AU - Sudhölter, Peter

PY - 2011/12

Y1 - 2011/12

N2 - It is well-known that the prenucleolus on the class of TU games is characterized by singlevaluedness, covariance under strategic equivalence, anonymity, and the reduced game property. We show that the prenucleolus on the class of TU games restricted to the connected coalitions with respect to communication structures may be characterized by the same axioms and a stronger version of independence of non-connected coalitions requiring that the solution does not depend on the worth of any non-connected coalition. Similarly as in the classical case, it turns out that each of the five axioms is logically independent of the remaining axioms and that an infinite universe of potential players is necessary. Moreover, a suitable definition and characterization of a prekernel for games with communication structures is presented.

AB - It is well-known that the prenucleolus on the class of TU games is characterized by singlevaluedness, covariance under strategic equivalence, anonymity, and the reduced game property. We show that the prenucleolus on the class of TU games restricted to the connected coalitions with respect to communication structures may be characterized by the same axioms and a stronger version of independence of non-connected coalitions requiring that the solution does not depend on the worth of any non-connected coalition. Similarly as in the classical case, it turns out that each of the five axioms is logically independent of the remaining axioms and that an infinite universe of potential players is necessary. Moreover, a suitable definition and characterization of a prekernel for games with communication structures is presented.

KW - IR-78766

KW - METIS-281614

KW - EWI-20929

KW - Solution concept

KW - TU game

KW - Nucleolus

KW - Communication and conference structure

M3 - Report

T3 - Memorandum / Department of Applied Mathematics

BT - The prenucleolus for games with communication structures

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -